Basic Math Examples

$\frac{1}{\frac{1}{2} + \frac{1}{6}}$

Step 1

Simplify the denominator.

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Step 1.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{\frac{1}{2} \cdot \frac{3}{3} + \frac{1}{6}}$

Step 1.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{1}{\frac{3}{2 \cdot 3} + \frac{1}{6}}$

Step 1.2.2

Multiply $2$ by $3$ .

$\frac{1}{\frac{3}{6} + \frac{1}{6}}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{1}{\frac{3 + 1}{6}}$

Step 1.4

Add $3$ and $1$ .

$\frac{1}{\frac{4}{6}}$

Step 1.5

Cancel the common factor of $4$ and $6$ .

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Step 1.5.1

Factor $2$ out of $4$ .

$\frac{1}{\frac{2 (2)}{6}}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $2$ out of $6$ .

$\frac{1}{\frac{2 \cdot 2}{2 \cdot 3}}$

Step 1.5.2.2

Cancel the common factor.

$\frac{1}{\frac{2 \cdot 2}{2 \cdot 3}}$

Step 1.5.2.3

Rewrite the expression.

$\frac{1}{\frac{2}{3}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{3}{2})$

Step 3

Multiply $\frac{3}{2}$ by $1$ .

$\frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$